Markov Random Field Research Articles

Ensemble Kalman filter with precision localization

AbstractWe propose a novel localization strategy for the ensemble Kalman filter procedure based on sparse precision matrices, which we denote precision localization. We assume the latent state vector to come from a Gaussian Markov random field and use the iterative proportional scaling algorithm to estimate the associated sparse precision matrix. Precision localization is compared against a standard covariance localization technique in two simulation studies; one with a Gauss-linear model and one based on the Lorenz 96 model. We evaluate the results by their prediction accuracy and to what degree the generated ensembles give a realistic representation of the exact filtering distributions. In the Gauss-linear example we also compare our results with the Kalman filter solution. Here we see that both precision and covariance localization produce reasonably good results in terms of prediction accuracy, but that precision localization provides the best representation of the correlation structure in the filtering distribution. For the Lorenz model we cannot compare with the Kalman filter solution, but precision localization seems to provide the most accurate predictions and the most realistic uncertainty representation.

Unsupervised object-based spectral unmixing for subpixel mapping

Subpixel mapping (SPM) addresses the widespread mixed pixel problem in remote sensing images by predicting the spatial distribution of land cover within mixed pixels. However, conventional pixel-based spectral unmixing, a key pre-processing step for SPM, neglects valuable spatial contextual information and struggles with spectral variability, ultimately undermining SPM accuracy. Additionally, while extensively utilized, supervised spectral unmixing is labor-intensive and user-unfriendly. To address these issues, this paper proposes a fully automatic, unsupervised object-based SPM (UO-SPM) model that exploits object-scale information to reduce spectral unmixing errors and subsequently enhance SPM. Given that mixed pixels are typically located at the edges of objects (i.e., the inner part of objects is characterized by pure pixels), segmentation and morphological erosion are employed to identify pure pixels within objects and mixed pixels at the edges. More accurate endmembers are extracted from the identified pure pixels for the secondary spectral unmixing of the remaining mixed pixels. Experimental results on 10 study sites demonstrate that the proposed unsupervised object (UO)-based analysis is an effective model for enhancing both spectral unmixing and SPM. Specifically, the spectral unmixing results of UO show an average increase of 3.65 % and 1.09 % in correlation coefficient (R) compared to Fuzzy-C means (FCM) and linear spectral mixture model (LSMM)-derived coarse proportions, respectively. Moreover, the UO-derived results of four SPM methods (i.e., Hopfield neural network (HNN), Markov random field (MRF), pixel swapping (PSA) and radial basis function interpolation (RBF)) exhibit an average increase of 5.89 % and 3.04 % in overall accuracy (OA) across the four SPM methods and 10 study sites compared to the FCM and LSMM-based results, respectively. Moreover, the proportions of both mixed and pure pixels are more accurately predicted. The advantage of UO-SPM is more evident when the size of land cover objects is larger, benefiting from more accurate identification of objects.

Advancing Credit Risk Management: The Adoption of Probabilistic Graphical Models in Banking

Assessment and management of credit risk at banks is a critical factor that ensures the stability and profitability of these institutions. Existing traditional statistical approaches that worked in the past are already proving to be incapable of coping with this new environment and the complexities intertwined within modern financial markets. Modern methodologies like probabilistic graphical models (PGMs) provide sophisticated methods for modeling these complex relationships, which integrate graph theory with probability theory. In this paper, we will explore Credit Risk and its main components, the mathematical foundation behind credit risk assessment, and the modeling techniques of these components. It compares traditional statistical models (eg, logistic regression and Monte Carlo simulations) with advanced Probabilistic Graphical models (PGMs). The paper highlights selecting the latter based on its capacity for more accurate representation of complex dependencies and uncertainties. PGMs that are covered here include Bayesian and Markov Networks, specifically for their structural representation of joint probability distributions, conditional independence as well as efficient inference. PGMs stand out for an improved model of non-linear interactions, and they allow the incorporation of uncertainty in a natural way, dynamic updating and systematic risk segmentation. This includes using Expectation-Maximization and Gradient-Based Optimization — bringing machine learning and modern computational methods to PGMs. It exemplifies the practical use of PGMs in credit risk management with examples ranging from default probability prediction to portfolio risk assessment and real-time risk monitoring. In conclusion, this paper points to the future promise of PGMs in credit risk management through continuing advancements in computation facilitated by embedding within an ML/AI framework. Reimagining This transformation will revolutionize how financial institutions measure and predict risks.

Methods for refining the depth map obtained from depth sensors

Depth maps are essential in applications such as robotics, augmented reality, autonomous vehicles, and medical imaging, providing critical spatial information. However, depth maps from sensors like time-of-flight (ToF) and structured light systems often suffer from low resolution, noise, and missing data. Addressing these challenges, this study presents an innovative method to refine depth maps by integrating high-resolution color images. The proposed approach employs both hard- and soft-decision pixel assignment strategies to adaptively enhance depth map quality. The hard-decision model simplifies edge classification, while the soft-decision model, integrated within a Markov Random Field framework, improves edge consistency and reduces noise. By analyzing discrepancies between edges in depth maps and color images, the method effectively mitigates artifacts such as texturecopying and blurred edges, ensuring better alignment between the datasets. Key innovations include the use of the Canny edge detection operator to identify and categorize edge inconsistencies and anisotropic affinity calculations for precise structural representation. The soft-decision model introduces advanced noise reduction techniques, improving depth map resolution and preserving edge details better than traditional methods. Experimental validation on Middlebury benchmark datasets demonstrates that the proposed method outperforms existing techniques in reducing Mean Absolute Difference values, especially in high-upscaling scenarios. Visual comparisons highlight its ability to suppress artifacts and enhance edge sharpness, confirming its effectiveness across various conditions. This approach holds significant potential for applications requiring high-quality depth maps, including robotics, augmented reality, autonomous systems, and medical imaging. By addressing critical limitations of current methods, the study offers a robust, versatile solution for depth map refinement, with opportunities for real-time optimization in dynamic environments.

Bayesian Inference for Long Memory Stochastic Volatility Models

We explore the application of integrated nested Laplace approximations for the Bayesian estimation of stochastic volatility models characterized by long memory. The logarithmic variance persistence in these models is represented by a Fractional Gaussian Noise process, which we approximate as a linear combination of independent first-order autoregressive processes, lending itself to a Gaussian Markov Random Field representation. Our results from Monte Carlo experiments indicate that this approach exhibits small sample properties akin to those of Markov Chain Monte Carlo estimators. Additionally, it offers the advantages of reduced computational complexity and the mitigation of posterior convergence issues. We employ this methodology to estimate volatility dependency patterns for both the SP&500 index and major cryptocurrencies. We thoroughly assess the in-sample fit and extend our analysis to the construction of out-of-sample forecasts. Furthermore, we propose multi-factor extensions and apply this method to estimate volatility measurements from high-frequency data, underscoring its exceptional computational efficiency. Our simulation results demonstrate that the INLA methodology achieves comparable accuracy to traditional MCMC methods for estimating latent parameters and volatilities in LMSV models. The proposed model extensions show strong in-sample fit and out-of-sample forecast performance, highlighting the versatility of the INLA approach. This method is particularly advantageous in high-frequency contexts, where the computational demands of traditional posterior simulations are often prohibitive.

A novel spatial heteroscedastic generalized additive distributed lag model for the spatiotemporal relation between PM2.5and cardiovascular hospitalization

Many studies have examined the impact of air pollution on cardiovascular hospitalization (CVH), but few have looked at the delayed effects of air pollution on CVH. Additionally, there has been no research on the spatial and temporal differences in how environmental pollutants affect CVH. This study seeks to identify spatial heteroscedasticity in the relation between PM2.5 and CVH by developing a Generalized Additive Distributed Lag (GADL) model. Data on hospitalization due to cardiovascular disease were collected from the Hospital Information System (HIS) of Mashhad University of Medical Science from 2017 to 2020. Air pollution data from 22 air quality monitoring (AQM) stations were obtained from the Environmental Pollution Monitoring Center of Mashhad administrates. Markov Random Field (MRF) smoother was utilized in the GADL model to account for spatial heteroscedasticity in the observations. This developed model is a Spatial Heteroscedastic Generalized Additive Distributed Lag (SHGADL) model. Our use of GADL allowed us to discover a significant relationship between PM2.5 exposures and the risk of CVH at lags 0 and 1 in all districts. Our results reveal heteroscedasticity in the Relative Risks (RR) of PM2.5 on CVH across different districts. After accounting for this spatial heteroscedasticity, we found that the RR of PM2.5 on CVH at lags 0 and 1 were 1.0102 (95% CI: 1.0034, 1.0170) and 1.0043 (95% CI: 1.0009, 1.0078) respectively. The central and southeastern districts showed higher RR for CVH. The developed SHGADL model provides evidence of a significant lagged effect of PM2.5 exposures on CVH, and identifies low- and high-risk districts for CVH in Mashhad. This finding can assist decision-makers in allocating resources and planning strategically, with a focus on local interventions to manage ambient air pollution and providing emergency care for CVH.

Uncovering adults' problem‐solving patterns from process data with hidden Markov model and network analysis

Uncovering adults' problem‐solving patterns from process data with hidden Markov model and network analysis

Model selection for Markov random fields on graphs under a mixing condition

We propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector. By global criterion, we mean optimizing a function over the set of possible graphs, eliminating the need to estimate individual neighborhoods and subsequently combine them to estimate the graph. We prove the almost sure convergence of the graph estimator. This convergence holds, provided the data is a realization of a multivariate stochastic process that satisfies a polynomial mixing condition. These are the first results to show the consistency of a model selection criterion for Markov random fields on graphs under non-independent data.

Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). BHRMs are popular for modeling complex dependence structures (e.g., Gaussian processes and Gaussian Markov random fields) but can be computationally expensive to run. Cross-validation (CV) is, therefore, not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to rerun computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. We shift the CV problem from probability-based sampling to a familiar and straightforward optimization problem by conditioning on the variance-covariance parameters. Our approximation applies to leave-one-out CV and leave-one-cluster-out CV, the latter of which is more appropriate for models with complex dependencies. In many cases, this produces estimates equivalent to full CV. We provide theoretical results, demonstrate the efficacy of our method on publicly available data and in simulations, and compare the model performance with several competing methods for CV approximation. Code and other supplementary materials available online.

Justification Models of Organizational and Technical Support of Measures to Create Information Protection System of Informatization Objects

The relevance of the article is due to the need to protect information at all stages of creating an information system in the absence of appropriate organizational and technical support. To justify this kind of provision, mathematical models are needed that take into account the conditions and the random nature of the implementation of heterogeneous information processing processes in time at each stage, threats to its security and protection from these threats. The article discusses approaches to the development of such models based on the apparatus of flow theory and the theory of composite Petri ‒Markov networks, the possibilities of which for modeling the processes under study have not been previously considered. The purpose of the article. To reveal the content of issues related to the justification of organizational and technical support for information protection at the stages of creating an information system, to show the need and ways to quantify threats to its security and protection from these threats. For this purpose, the methods of functional and structural analysis, probability theory and flow theory were applied. In the course of solving the scientific problem, the relevance of substantiating the organizational and technical support of information protection at the stages of creating information systems is shown, descriptive models of its processing processes are developed, time diagrams of threat scenarios are given in the absence of protection measures and in the conditions of using preventive organizational and technical measures, indicators and analytical ratios for their calculation are proposed. The scientific novelty of the article consists in the fact that for the first time it examines the issues of organizational and technical support for information protection at the stages of creating an information system, examines the theoretical aspects of quantifying threats to its security and protection from these threats based on flow theory and prospects for applying the theory of composite Petri-Markov networks. Significance (theoretical). The conditions for the implementation of the studied processes and the possibility of applying the theory of flows and the apparatus of composite Petri–Markov networks for their modeling are established. Significance (practical). The results obtained in the work can be used to justify the organizational and technical provision of information protection at the stages of creating information systems of various organizations (both state and non-state), for which the implementation of threats at these stages may lead to damage to their activities.

Non-stationary spatio-temporal modeling using the stochastic advection–diffusion equation

We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation of the solution of the SPDE, which is constructed through a finite volume method. The new flexible non-separable model is compared to a flexible separable model both for reconstruction and forecasting, and evaluated in terms of root mean square errors and continuous rank probability scores. A simulation study demonstrates that the non-separable model performs better when the data is simulated from a non-separable model with diffusion and advection. Further, we estimate surrogate models for emulating the output of a ocean model in Trondheimsfjorden, Norway, and simulate observations of autonomous underwater vehicles. The results show that the flexible non-separable model outperforms the flexible separable model for real-time prediction of unobserved locations.

Markov field network model of multi-modal data predicts effects of immune system perturbations on intravenous BCG vaccination in macaques.

Analysis of multi-modal datasets can identify multi-scale interactions underlying biological systems but can be beset by spurious connections due to indirect impacts propagating through an unmapped biological network. For example, studies in macaques have shown that Bacillus Calmette-Guerin (BCG) vaccination by an intravenous route protects against tuberculosis, correlating with changes across various immune data modes. To eliminate spurious correlations and identify critical immune interactions in a public multi-modal dataset (systems serology, cytokines, and cytometry) of vaccinated macaques, we applied Markov fields (MFs), a data-driven approach that explains vaccine efficacy and immune correlations via multivariate network paths, without requiring large numbers of samples (i.e., macaques) relative to multivariate features. We find that integrating multiple data modes with MFs helps remove spurious connections. Finally, we used the MF to predict outcomes of perturbations at various immune nodes, including an experimentally validated B cell depletion that induced network-wide shifts without reducing vaccine protection.

Markov Field network model of multi-modal data predicts effects of immune system perturbations on intravenous BCG vaccination in macaques.

Analysis of multi-modal datasets can identify multi-scale interactions underlying biological systems, but can be beset by spurious connections due to indirect impacts propagating through an unmapped biological network. For example, studies in macaques have shown that BCG vaccination by an intravenous route protects against tuberculosis, correlating with changes across various immune data modes. To eliminate spurious correlations and identify critical immune interactions in a public multi-modal dataset (systems serology, cytokines, cytometry) of vaccinated macaques, we applied Markov Fields (MF), a data-driven approach that explains vaccine efficacy and immune correlations via multivariate network paths, without requiring large numbers of samples (i.e. macaques) relative to multivariate features. Furthermore, we find that integrating multiple data modes with MFs helps to remove spurious connections. Finally, we used the MF to predict outcomes of perturbations at various immune nodes, including a B-cell depletion that induced network-wide shifts without reducing vaccine protection, which we validated experimentally.

Hybrid-driven MRF seismic inversion for gas sand identification: A case study in the Yinggehai Basin

The Yinggehai Basin displays anomalies characterized by heightened levels of temperature and pressure. It represents a depositional model of a submarine fan with gravity-driven flow, demonstrating significant lateral reservoir heterogeneity and intricate spatial distribution of the gas reservoir. Identifying gas formations using elastic parameters as indicators relies on stable seismic inversion results. This requires regularization to alleviate ill-posedness in the inverse problem and to construct model features of the subsurface medium. Markov Random Field (MRF)is an effective soft-constrained regularization method. It enhances the marginal features of inversion results by penalizing the objective function with the gradient of neighborhood points. However, the standard MRF method relies only on the parameter model-driven and has poor applicability in areas with strong lateral inhomogeneity or complex depositional processes. In this research paper, we propose a novel approach to seismic inversion that integrates MRF neighborhood drive and incorporates both seismic data and a parametric model. Multi-order MRF neighborhoods are constructed by using seismic data in the horizontal direction (including horizontal diagonal) and parametric model data in the vertical direction (including vertical diagonal). The model-driven results are also utilized to couple seismic data and improve the stability of the hybrid-driven MRF inversion. In addition, we select the P-impedance as the parameter for inversion due to its heightened sensitivity towards gas formation within the study region. Consequently, we utilize the inversion results to delineate the presence of sandstone in the target layer and discern any indications of gas formation. The implementation of this method in the field has demonstrated its capability to enhance the stability of inversion outcomes, effectively integrating the lateral consistency of seismic data with the vertical precision of parametric model data. This approach significantly improves reservoir heterogeneity characterization and enhances accuracy in identifying sandstone and gas.

Protein language models learn evolutionary statistics of interacting sequence motifs

Protein language models (pLMs) have emerged as potent tools for predicting and designing protein structure and function, and the degree to which these models fundamentally understand the inherent biophysics of protein structure stands as an open question. Motivated by a finding that pLM-based structure predictors erroneously predict nonphysical structures for protein isoforms, we investigated the nature of sequence context needed for contact predictions in the pLM Evolutionary Scale Modeling (ESM-2). We demonstrate by use of a "categorical Jacobian" calculation that ESM-2 stores statistics of coevolving residues, analogously to simpler modeling approaches like Markov Random Fields and Multivariate Gaussian models. We further investigated how ESM-2 "stores" information needed to predict contacts by comparing sequence masking strategies, and found that providing local windows of sequence information allowed ESM-2 to best recover predicted contacts. This suggests that pLMs predict contacts by storing motifs of pairwise contacts. Our investigation highlights the limitations of current pLMs and underscores the importance of understanding the underlying mechanisms of these models.

Reference to Patients in Nurse Shift Handover Meetings: Exploring the Dynamics of Referring Expressions

ABSTRACT This paper investigates the dynamics of referring expressions in hospital nurse handover meetings when discussing patients. We apply the methods of the Variable Length Markov Chain (VLMC) and network analyses to model the use of referring expressions and evaluate relationships between them. The models reveal second-order dependencies emerging for metonymy and noun phrases. Specifically, metonymy shows a greater association with the beginning of a reference, particularly in the context of other metonymies. In contrast, noun phrases tend to be more strongly associated with later points in the reference. Further, we introduce the notion of referential typicality, which measures the conformity of sequences of referring expressions to anticipated patterns. We show, for example, that consecutive noun phrases fall outside the typical pattern, whereas metonymical sequences and sequences of pronouns are highly typical. The transitions from metonymy or nouns to pronouns also closely align with a highly typical pattern. Using a Generalized Additive Model (GAM), we then track the overall evolution of referential typicality throughout the duration of handover meetings, from their beginning to end. The study reveals a subtle increase in referential typicality towards the end of these sessions, indicating a trend towards more consistent referencing as the discourse unfolds.

A real scale application of a novel set of spatial and similarity features for detection and classification of natural seismic sources from distributed acoustic sensing data

SUMMARY Distributed acoustic sensing (DAS) turns a fibre optic into a very dense network of equally distributed seismic sensors. We focused on the high-density sampling of the seismic wavefield, expressed in strain rates, measured by DAS. Classical approaches used to identify seismic signals rely on the recorded features at one station, but it is difficult to include spatial information in case of dense seismic station networks. This work aims at introducing new spatial and similarity features for seismic event classification suitable to analyse DAS observations. We propose a processing chain based on the XGBoost algorithm and the use of specifically designed spatiotemporal and similarity features for the event classification, and Markov random field for the spatial clustering. The methodology is designated to be applied on a continuous stream of DAS observations. We tested our processing chain to detect earthquakes and quarry blasts recorded in the region by permanent seismic networks and included in the RENASS catalogue. These events are part of a strain-rate seismic survey carried out during a 3 weeks campaign of DAS measurements along à 91 km fibre optic cable deployed in the central Pyrenees mountains (France). Despite the high anthropogenic activities along the fibre optic path, the proposed method succeeded in detecting earthquakes of magnitude >0.4 and quarry blasts of magnitude >1.0 while limiting the number of false alarms. This performance is particularly noteworthy for low-magnitude events, where detection is accomplished despite a lower signal-to-noise ratio compared to traditional seismometers. The methodology opens the door to real time detection and classification of seismic events measured with long-distance fibre optic systems.

AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks.

Remote Sensing Image Segmentation Based on Probabilistic Fuzzy Local Information Clustering

Abstract. In this paper, a remote sensing image segmentation based on probabilistic fuzzy local information clustering algorithm is proposed. First, assuming that the spectral measure within the same ground object follows the same probability distribution. The dissimilarity between pixel and object is modeled by the negative logarithm of the Gaussian probability density function. It can improve the noise sensitive problem caused by the Euclidean distance which can only describe the data with isotropic distribution. Then, in order to consider the effect of local spatial constraint, on the one hand, the probability measure is used to modify the local fuzzy factor to establish the dissimilarity measure with spatial constraints. On the other hand, the hidden Markov random field is used to model the prior probability model of pixel membership. Next, the entropy regularization term of the objective function is built by combining the Kullback-Leibler(KL) maximum entropy model to further improve the robustness and noise resistance. The qualitative and quantitative analysis of simulated image and different types of real remote sensing images show that the proposed algorithm can effectively overcome the above problems and further improve the accuracy of image segmentation to over 95%.

Improved MRF rail surface defect segmentation method based on clustering features

Aiming at the characteristics of small number and many types of rail surface defect samples, as well as the problems of unstable transfer learning effect and threshold segmentation being easily affected by environmental factors in real scenes, an improved Markov defect segmentation method with zero samples is proposed. Firstly, the collected data is processed by Gabor function to highlight the defect features and reduce the data dimension to obtain the reduced dimension feature map; Kmeans clustering is performed on the processed feature map to reduce the distribution of data and reduce the influence of reflection and shadow, and the clustering result is used as the pre-classification matrix; an improved Markov random field two-layer graph model is constructed and inferred through the reduced dimension feature map and the pre-classification matrix; the local geometric structure of the defect part is analyzed according to the eigenvalues of the classification matrix inferred by the model; finally, the defect area is marked and the defect segmentation is completed. The experimental part uses a self-sampling data set, and the final conclusion is drawn based on the comparative experiment and ablation experiment. The experimental results show that the pixel accuracy, average pixel accuracy, weighted intersection-over-union ratio, and average intersection-over-union ratio of this method on the self-sampling data set are respectively 93.6%、80.7%、89.4%、68.2% , which exceeds the accuracy of other comparative detection algorithms.